Among those arrested were a 23-year-old Colombian woman and 27-year-old Swiss man, both targets of a Swiss investigation into banned Islamic extremist groups.
Searches are still underway in the Paris suburbs and in southeastern France.
Counterterrorism investigators detained nine people in France and one in Switzerland in operations aimed at clarifying details of the suspected plot, according to a French judicial official. The official, who spoke on condition of anonymity to discuss an ongoing investigation, would not provide details about their identities.
In parallel to the Swiss investigation, French authorities opened a probe in July focused on suspicious activity by a person in Switzerland using the Telegram network, according to a French judicial official. The Swiss-based chief suspect had communicated with people in France on social networks about unspecified violent acts, the official said.
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A French security official said the suspected plot did not appear to be fully developed but authorities acted Tuesday out of concern that the group was moving toward action.
Among French towns targeted in the operation were Aix-en-Provence in southern France and Menton on the Mediterranean coast as well as Paris suburbs, according to the security official.
The office of Swiss Attorney General Michael Lauber said the arrest there followed searches of buildings in the French-speaking Vaud and Neuchatel regions of western Switzerland.
The Swiss investigation had originally targeted a 27-year-old Swiss man and was more recently extended to include the Colombian woman, neither of whom was identified by name. Lauber's office said the woman is expected to remain in custody until she appears before a court. The Swiss man was among those arrested in France.
A joint investigation team has been created in the case by authorities in the two countries.
The operation comes days after a new counterterrorism law came into effect in France to replace a state of emergency that had been in place since deadly attacks in Paris two years ago.
French Interior Minister Gerard Collomb appeared to downplay the arrests, telling reporters during a visit to Germany on Tuesday that, "in a relatively habitual way, we arrest a certain number of individuals who appear that they could be dangerous."